arXiv subjects

Hyeong-Ohk Bae

Publications and source records attributed to Hyeong-Ohk Bae.

7 recordsLinked to original sources

arXiv2026

CBO algorithm with average drift and applications to portfolio optimization

We propose a consensus based optimization algorithm with average drift (in short Ad-CBO) and provide a theoretical framework for it. In the theoretical analysis, we show that particle solutions to Ad-CBO converge to a global minimizer. In numerical simulations, we examine Ad-CBO's performance in optimizing static and dynamic objective functions. As a real-time application, we test the efficiency of Ad-CBO to find the optimal portfolio given stochastically evolving multi-asset prices in a financial market. The proposed Ad-CBO exhibits higher searching speed, lower tracking errors and regret bound than the CBO without stochastic diffusion

math.OC↗

arXiv2023

Physics-Informed Convolutional Transformer for Predicting Volatility Surface

Predicting volatility is important for asset predicting, option pricing and hedging strategies because it cannot be directly observed in the financial market. The Black-Scholes option pricing model is one of the most widely used models by market participants. Notwithstanding, the Black-Scholes model is based on heavily criticized theoretical premises, one of which is the constant volatility assumption. The dynamics of the volatility surface is difficult to estimate. In this paper, we establish a novel architecture based on physics-informed neural networks and convolutional transformers. The performance of the new architecture is directly compared to other well-known deep-learning architectures, such as standard physics-informed neural networks, convolutional long-short term memory (ConvLSTM), and self-attention ConvLSTM. Numerical evidence indicates that the proposed physics-informed convolutional transformer network achieves a superior performance than other methods.

q-fin.CP↗

arXiv2023

Mathematical modeling of trend cycle: Fad, Fashion and Classic

In this work, we suggest a system of differential equations that quantitatively models the formulation and evolution of a trend cycle through the consideration of underlying dynamics between the trend participants. Our model captures the five stages of a trend cycle, namely, the onset, rise, peak, decline, and obsolescence. It also provides a unified mathematical criterion/condition to characterize the fad, fashion and classic. We prove that the solution of our model can capture various trend cycles. Numerical simulations are provided to show the expressive power of our model.

math.AP↗

arXiv2021

A Constrained Consensus Based Optimization algorithm and its Application to Finance

In this paper, we propose a predictor-corrector type Consensus Based Optimization (CBO) algorithm on a convex feasible set. Our proposed algorithm generalizes the CBO algorithm in [11] to tackle a constrained optimization problem for the global minima of the non-convex function defined on a convex domain. As a practical application of the proposed algorithm, we study the portfolio optimization problem in finance. In this application, we introduce an objective function to choose the optimal weight on each asset in a asset-bundle which yields the maximal expected returns given a certain level of risks. Simulation results show that our proposed predictor-corrector type model is successful in finding the optimal value.

math.OC↗

arXiv2019

A kinetic description for the herding behavior in financial market

As a continuation of the study of the herding model proposed in (Bae et al. in arXiv:1712.01085, 2017), we consider in this paper the derivation of the kinetic version of the herding model, the existence of the measure-valued solution and the corresponding herding behavior at the kinetic level. We first consider the mean-field limit of the particle herding model and derive the existence of the measure-valued solutions for the kinetic herding model. We then study the herding phenomena of the solutions in two different ways by introducing two different types of herding energy functionals. First, we derive a herding phenomena of the measure-valued solutions under virtually no restrictions on the parameter sets using the Barbalat's lemma. We, however, don't get any herding rate in this case. On the other hand, we also establish a Grönwall type estimate for another herding functional, leading to the exponential herding rate, under comparatively strict conditions. These results are then extended to smooth solutions.

math.AP↗

arXiv2017

A particle model for the herding phenomena induced by dynamic market signals

In this paper, we study the herding phenomena in financial markets arising from the combined effect of (1) non-coordinated collective interactions between the market players and (2) concurrent reactions of market players to dynamic market signals. By interpreting the expected rate of return of an asset and the favorability on that asset as position and velocity in phase space, we construct an agent-based particle model for herding behavior in finance. We then define two types of herding functionals using this model, and show that they satisfy a Gronwall type estimate and a LaSalle type invariance property respectively, leading to the herding behavior of the market players. Various numerical tests are presented to numerically verify these results.

q-fin.CP↗

arXiv2014

On the effect of external forces on incompressible fluid motions at large distances

We study incompressible Navier--Stokes flows in~$\R^d$ with small and well localized data and external force~$f$. We establish pointwise estimates for large~$|x|$ of the form \hbox{$c_t|x|^{-d}\le |u(x,t)|\le c'_t|x|^{-d}$}, where $c_t>0$ whenever $\int_0^t\!\!\int f(x,s)\,dx\,ds\not=\vec 0$. This sharply contrasts with the case of the Navier--Stokes equations without force, studied in [Brandolese, Vigneron, J. Math. Pures Appl. 88, 64--86 (2007)], where the spatial asymptotic behavior was $|u(x,t)|\simeq C_t|x|^{-d-1}$. In particular, this shows that external forces with non-zero mean, no matter how small and well localized (say, compactly supported in space-time), increase the velocity of fluid particles at {\it all times~$t$} and at \emph{at all points~$x$} in the far-field. As an application of our analysis on the pointwise behavior, we deduce sharp upper and lower bounds of weighted $L^p$-norms for strong solutions, extending the results obtained in [Bae, Brandolese, Jin, Asymptotic behavior for the Navier--Stokes equations with nonzero external forces, Nonlinear analysis, doi:10.1016/j.na.2008.10.074] for weak solutions, by considering here a larger (and in fact, optimal) class of weight functions.

math.AP↗